Identification for Insulin Signal Kinetics in HEK293 Cells via Mathematical Modeling

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Identification for Insulin Signal Kinetics in
HEK293 Cells via Mathematical Modeling

• Department of Mathematics. POSTECH Kwang Ik
  Kim
• Department of Life Science, POSTECH Sung Ho
  Ryu

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Introduction

• Insulin signal transduction is a signaling path
  process from external stimulus to a cellular
  response.
• The fundamental motif in signaling network is the
  phosphorylation and dephosphorylation which have
  a dynamic profile.

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Introduction

• To identify the dynamics of insulin signal
  transduction system, a mathematical model, which
  governs the signal transduction from an
  extracellular stimulation to the activation of
  intracellular signal molecules is constructed.
• In insulin signal transduction, each signal
  protein has its own kinetic profile in such a way
  that IR, IRS , Akt and Erk are phosphorylated
  transiently.

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Introduction

• These kinetic profiles are determined by their
  kinases and phosphatases appropriately for their
  physical roles in insulin signal transduction.
• Through this system, it is possible to predict
  each signaling proteins quantitatively, once the
  concentration of treated insulin is given, which
  is very important to regulate the pharmaceutical
  control of insulin concentration

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Kinetic scheme of insulin-induced insulin
receptor signaling cascade
Insulin-bound insulin receptor initiates
important signal transductions, IRS-PI3K-PDK-Akt
and IRS- Ras-Raf-MEK-ERK pathways ,
mass action
MKP3
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Simplified kinetic model of insulin signaling
Insulin
k1
IR
IR
E1
k2
k3
IR-E1
k-2
E1
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Basic module in signal transduction
Michelis-Menten forward and backward kinetics
dp/dt k2E1S / (KMS) 4E2P /
(KMP ) , where KM(k-1k2) / k1,
KM(k-3k4)/k3
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Kinetic equation in insulin signal transduction
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Kinetic equations modified from the insulin
signal transduction kinetics
dIR / dt k1IIR k3E10IR /
(K2IR)
dIRS / dt k5IR0IRS / (K3IRS)
k7E20IRS / (K4IRS)
dAkt / dt k9IRS0Akt / (K5Akt)
k11E30Akt / (K6Akt)
dERK / dt k13IRS0ERK / (K7ERK)
k15E40ERK / (K8ERK)
Where K2 (k-2k3) / k2, K3 (k-4k5) / k4,
K4 (k-6k7) / k6, K5 (k-8k9) / k8, K6
(k-10k11) / k10, K7 (k-12k13) / k12, K8
(k-14k15) / k14
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Experimental materials and methods

• 1. Cell preparation
• HEK 293 cells were subcultured in 6cm tissue
  dishes with Dulbeccos Modified
• Eagle Medium (DMEM) containing 10 fetal
  bovine serum.
• 2. Fasting
• Dishes to be processed on the same day were
  plated with equal number of
• cells. The cells were incubated for 24h in
  DMEM.

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Experimental materials and methods

• 3. Insulin Stimulation
• At various times, insulin was added to each
  plate at the final concentration
• indicated and incubated for the time interval
  specified. At the end point of
• the experiment, each plate was washed twice
  with ice-cold Dulbeccos
• phosphate buffered saline and lysed in 150nM
  of ice-cold buffer containing
• 40mM HEPES.
• 4. Sonication
• Each lysate transferred to Eppendorf tube
  after scapping was sonicated and
• contrifuged at 4 C for 15 min to acquire
  supernatant. The protein concentration
• of each lysate was measured by Bradford
  assay.

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Experimental materials and methods

• 5. Centrifugation
• To quantify the phosphorylation of signal
  proteins, cell lysate samples
• containing equal amounts of proteins were
  resolved by SDS-PAGE and
• electrophoretically transferred to
  nitrocellulose membrane.

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Experimental materials and methods

• 6. Electrophoresis

NC
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Experimental Materials and Methods

• 7. Antibody
• After blocking with 5 skimmed milk in TTBS (10
  mM Tris/HCl, pH7.5, 150 mM
• NaCl and 0.5 (w/v) tween 20), the membranes
  were incubated with the antibodies
• (anti-phospho-IRS, anti-phospho-IR,
  anti-phospho-Akt, anti-phospho-ERK and
• anti-actin). Washed with TTBS, the membranes
  were incubated with peroxidase-
• conjugated goat anti-rabbit IgG (KPL) and
  peroxidase-conjugated goat anti-mouse
• IgAIgGIgM (HL) (KPL).
• 8. Quantitative Analysis
• To visualize the phosphorylated proteins, the
  enhanced chemillominescence system
• (ECL system from Amersham Corp.) was used and
  proteins bands were quantified
• using densidomiter (Fuji-Film Corp.)

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Phosphorylation patterns of signal proteins with
respect to insulin stimulation time
HEK 293 cells are deprived of serum for 24h
before treatment and stimulated with 10 nM and
100 nM of insulin for indicated time and
lysed.The lysates are subjected to SDS-PAGE and
immunoblotted. A HEK 293 cells are stimulated
with 10 nM of insulin. B HEK 293 cells are
stimulated with 100 nM of insulin.
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Regresstion with in vivo data via least squares
method for p-IR
(B)
(A)
10 nM a2.78201
10 nM b0.68833
100 nM a1.39433
100 nM b0.54915
Graphs from in vivo experimental data and in
silico analysis (A) Based on the in vivo data,
kinetic graphs for insulin signal proteins
were drawn. (B) After regression with in vivo
data, in silico graph were obtained.
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Regresstion with in vivo data via least squares
method for p-IRS
10 nM a0.83907
10 nM b1.32975
100 nM a0.25139
100 nM b0.91993
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Regresstion with in vivo data via least squares
method for p-Akt
1.4
1.2
1
0.8
0.6
0.4
10nM Insulin
100nM Insulin
0.2
0
0
5
10
15
20
10 nM ymax0.85000
10 nM a2.25335
100 nM ymax1.06250
100 nM a4.44860
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Regresstion with in vivo data via least squares
method for p-ERK
10nM a0.35000
10nM b0.17241
10nM c0.57564
10nM d0.17306
10nM f- 0.71380
10nM g- 0.00992
100nM a0.86600
100nM b0.02858
100nM c0.35690
100nM d0.78620
100nM f- 0.71380
100nM g- 0.01272
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Kinetic graphs for p-IR in vivo and in silico
least squares fitted data
p-IR In silico fitted data
p-IR In vivo experimental data
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Kinetic graphs for p-IRS in vivo and in silico
least squares fitted data
p-IRS least squares fitted data
p-IRS In vivo data
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Kinetic graphs for p-Akt in vivo and in silico
least squares fitted data
p-Akt In vivo data
p-Akt least squares fitted data
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Kinetic graphs for p-ERK in vivo and in silico
least squares fitted data
p-ERK In vivo data
p-ERK least squares fitted data
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Relative kinetic graphs for phosphorylation of IR
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Relative kinetic graphs for phosphorylation of IRS
Phosphorylation of 10nM IRS
Phosphorylation of 100nM IRS
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Relative kinetic graphs for phosphorylation of Akt
Phosphorylation of 100nM Akt
Phosphorylation of 10nM Akt
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Relative kinetic graphs for phosphorylation of ERK
Phohphorylation of 10nM ERK
Phohphorylation of 10nM ERK
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Linearlized System for Insulin Signaling Kinetics
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Reaction coefficients Identified via
Pseudo-Inverse with Householder transformation
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Identified reaction coefficients and p-IR signal
proteins
p-IR with K1 and k3IR for 10 nM insulin
p-IR with K1 and k3IR for 100 nM insulin
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Reaction coefficients Identified via
Pseudo-Inverse with Householder transformation
k5
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Identified reaction coefficients versus p-IRS
signal proteins
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Reaction coefficients Identified via
Pseudo-Inverse with Householder transformation
AKt
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Identified reaction coefficients versus p-Akt
signal proteins
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Reaction coefficients Identified via
Pseudo-Inverse with Householder transformation
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Identified reaction coefficients and p-ERK signal
proteins
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Interpolation with identified parameters for 30nM
insulin concentration
Predicted p-IR protein signal for 30 nM insulin
Predicted p-IRS protein signal for 30 nM insulin
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Interpolation with identified parameters for 30nM
insulin concentration
Predicted p-Akt protein signal for 30 nM insulin
Predicted p-ERK protein signal for 30 nM insulin
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Phosphorylation pattern of signal proteins for
30nM insulin stimulation
HEK 293 cells are deprived of serum for 24h
before treatment and stimulated with 30 nM
insulin for indicated time. HEK 293 cells are
stimulated with 30 nM of insulin.
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Regresstion with in vivo data via least squares
method for protein signals
Regression parameters for 30 nM insulin concentration by least squares method Regression parameters for 30 nM insulin concentration by least squares method Regression parameters for 30 nM insulin concentration by least squares method
p-IR a1.87940
p-IR b0.58406
p-IRS a0.76379
p-IRS b1.33801
p-Akt ymax0.9000
p-Akt a3.03422
p-ERK a0.33628
p-ERK b0.00669
p-ERK c0.57565
p-ERK d0.22306
p-ERK f- 1.72694
p-ERK g- 0.00634
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Regression with 30nM invivo data via least
squares method
p-IRS
p-IR
1.2
2.5
1
2
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0.8
1.5
0.6
1
0.4
0.5
0.2
0
0
0
5
10
15
20
0
5
10
15
20
p-Akt
p-ERK
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Regression with 30nM invivo data via least
squares method
1.2
2.5
1
2
0.8
1.5
0.6
1
0.4
0.5
0.2
0
0
0
5
10
15
20
0
5
10
15
20
p-Akt
p-ERK
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Comparison with predicted and least squares
fitted data
p-IR
p-IRS
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Comparison with predicted and least squares
fitted data
p-Akt
p-ERK
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Conclusion

• Kinetics for Insulin transduction is identified.
• It is possible to predict IR, IRS, Akt,
  and ERK
• without actural experiment

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Future Study
More invivo data for different Insulin medication
cases are necessary to verify the effectiveness
of our results.
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